There could also be attractor states that reduce the risk. For example in this case (if the numbers are taken to be such that the EV is positive) then you can also end up with a lucky player getting rich. The chance of that player going bust goes down much lower than the chance for a new player starting with $1. So while individual players may tend to go bust reliably, the total pool of wealth can still grow beyond any set upper boundary. Over time each player tends to get fabulously rich or go bust, so the game is mostly one of whether an initial run of luck gets you out of the danger zone before running into zero.

If you added some effects on what kind of gambles are available to players at different levels, you can create several different attractor states.

Ergodicity is a nice property of models like molecules of gas bouncing around a room, which means that statistical mechanics is practical. If one percent of the molecules tended to end up with all the kinetic energy, while the other molecules gradually one by one reached a complete standstill, then statistical mechanics wouldn't work.

Since the very simple process shown in the article doesn't have this property, it means some familiar statistical tools can't be used naively with these models, or to extrapolate a little bit, to any model of any human activity that tends to these kinds of capturing, fixed-point, attractor outcomes.